Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001521
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Mapping
St001521: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => 3
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([],5)
 => 0
([(3,4)],5)
 => 3
([(2,4),(3,4)],5)
 => 5
([(1,4),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 6
([(1,4),(2,3)],5)
 => 2
([(1,4),(2,3),(3,4)],5)
 => 5
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,3),(3,4)],5)
 => 5
([(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 5
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
Description
Half the total irregularity of a graph. This is half the sum of the absolute values of the degree differences of all pairs of vertices: $$ \frac{1}{4}\sum_{u,v} |d_u-d_v| $$ It is easy to show by induction on the number of edges that this is an integer.